1. Field of the Invention
The present invention relates to a method and an apparatus for measuring a reflectance of specular reflection, i.e., total reflection, of an X-ray which is reflected by a surface of a sample, and especially to a method and an apparatus for X-ray reflectance measurement in which a correct value of an incident angle to the sample surface can be determined accurately to realize high-accurate reflectance measurement.
2. Description of the Related Art
Some methods are known for measuring a thickness of a thin film deposited on a substrate. Of these methods, an X-ray reflectance method is in the spotlight because it can determine the absolute value of the thickness and also it is nondestructive. Although the X-ray reflectance method has the advantages of the determination of the absolute value of the thickness and the nondestructive measurement, the observed thickness determined by the current X-ray reflectance method is said to be inferior, in view of repeatability, to that obtained by the X-ray photoelectron spectroscopy method or the ellipsometry method. If the repeatability of the thickness is improved in the X-ray reflectance method, the X-ray reflectance method could be the hopeful standard method for the thickness measurement.
There are many publications disclosing the determination of the thickness and/or the density of the thin film with the use of the X-ray reflectance method, the examples being Japanese patent publication No. 2000-35408 A and Japanese patent publication No. 11-258185 A (1999).
The inferior repeatability of thickness in the X-ray reflectance method is attributed to inaccurate determination of the incident angle of the incident X-ray which is incident on the surface of the thin film sample. It will be explained in detail below.
FIG. 1A is a plan view showing an X-ray path under the condition in which the X-ray optical system of the X-ray reflectance measurement apparatus is in the state of 2θ=0. Defining an angle of the reflected X-ray to the incident X-ray 10, i.e., a scattering angle, as 2θ, the state of 2θ=0 can be said to be the state in which the incident X-ray 10 is directly incident on an X-ray detector 12. The incident X-ray 10 has been positioned so as to pass through the center O of the goniometer. The X-ray detector 12 can rotate around the goniometer center O and its rotation angle is 2θ. An angle of incident X-ray 10 to the surface of a sample 16 is defined as an incident angle ω. The sample 16 also can rotate around the goniometer center O and its rotation angle is equal to ω. The position of the sample 16 is adjusted, with the use of the conventional half-split method, so as to allow its surface to coincide with the goniometer center O. If the surface of the sample 16 is positioned just on the goniometer center O, the incident angle ω is accurately equal to the rotation angle of the sample 16, so that the accuracy of the observed incident angle ω would be the same as the accuracy of the angle determination of the drive mechanism for the rotation of the sample 16. It is very difficult, however, from a practical standpoint to allow the position of the sample surface to coincide with the goniometer center O with accuracy of less than one micrometer. Discussing the error δW in positioning the sample 16, this error δW is expressed by a distance between the goniometer center O and the surface of the sample 16. The existence of such error δW causes deterioration in accuracy of the observed incident angle ω.
FIG. 1B shows a condition in which an X-ray reflectance is measured for the sample 16 having the above-described positioning error δW. The X-ray reflectance is measured with the following steps: the sample 16 is rotated in ω-rotation while the X-ray detector 12 is rotated in 2θ-rotation with a relationship of ω: 2θ=1:2; and an X-ray intensity of the specular reflection, i.e., total reflection, from the surface of the sample 16 is detected. Defining the observed value of the scattering angle 2θ as 2θm, the angle 2θm is equal to the rotation angle of the X-ray detector 12 around the goniometer center O. A receiving slit 18 is disposed in front of the X-ray detector 12 and is rotated synchronously with the X-ray detector 12. The aperture width of the receiving slit 18 is set to be narrow. The scattering angle 2θm of the specular reflection is very small, usually less than several degrees, or over ten degrees at largest. The rotation angle ω of the sample 16, i.e., the incident angle ω, is scanned within a small range in the vicinity of the half of 2θm, so that the intensity of a reflected X-ray 20 detected by the X-ray detector 20 varies and the observed incident angle ω can be determined at the maximum intensity. Then, the observed incident angle ω is scanned, i.e., the scattering angle 2θ is scanned, to obtain the intensity of the reflected X-ray for each incident angle. The reflected X-ray intensities are plotted versus the incident angles to make an X-ray reflectance curve.
Defining a real incident angle of the incident X-ray 10 to the sample surface as ωa, it is difficult to know the real incident angle ωa with high accuracy, because it is difficult, with measurement, to determine the origin of the incident angle ω with high accuracy, the origin being defined as the condition in which the incident X-ray 10 becomes perfectly parallel to the sample surface. Then, in the conventional method, it has been assumed that the real incident angle ωa is equal to the half of the observed value 2θm of the scattering angle 2θ, because, in principle in the specular reflection, the incident angle is just equal to the half of the scattering angle.
However, since there exits the positioning error δW of the sample 16 as described above, the observed value 2θm of the scattering angle is different from the real scattering angle 2θa. Now, the difference between 2θm and 2θa is expressed by δ(2θ), that is, 2θa=2θm+δ(2θ). The observed value 2θm is an angle measured around the goniometer center O, while the real scattering angle is an angle of the reflected X-ray 20 to the incident X-ray 10 around the real X-ray irradiation point P on the sample surface. The direction of the reflected X-ray 20, i.e., the angle of the reflected X-ray 20, is determined by the position of the receiving slit 18. The distance D between the goniometer center O and the X-ray irradiation point P causes the above-described difference δ(2θ).
Estimation for δ(2θ) will be explained below. The distance D is found with formula (1) in FIG. 2. A tangent of the difference δ(2θ) is found with formula (2) in FIG. 2, noting that L is the distance between the goniometer center O and the receiving slit 18. Since δ(2θ) is very small, tan δ(2θ) is almost equal to δ(2θ), provided that δ(2θ) is expressed in units of radian. Thus, the left side of formula (2) becomes δ(2θ). On the other hand, in the right side of formula (2), since D is much smaller than L, the denominator is almost equal to L. Therefore, formula (2) comes near to formula (3).
As shown in formula (4), the real incident angle ωa is just equal to the half of the real scattering angle 2θa which is different from the observed value 2θm by the difference δ(2θ). Accordingly, if the incident angle is determined based on 2θm (the thus-determined incident angle being referred to as ωm hereinafter), the observed incident angle ωm is different from the real incident angle ωa as shown in formula (5). In the conventional method, a reflectance curve is obtained based on the observed incident angle ωm which is different from the real incident angle ωa, and then the thickness of the thin film is determined based on the reflectance curve, resulting in insufficient repeatability of the thickness measurement.
The value of δ(2θ) will be discussed with applying suitable values to the above-described formula (3). The positional error δW of the sample is assumed to be one micrometer. If the position of the sample is adjusted with the usual half-split method, the positional error would be not so large, but it is difficult to position the sample with accuracy of less than one micrometer. The angle 2θm is assumed to be 0.6 degree, and the angle ω is assumed to be 0.3 degree which is the half of 2θm. These values are applied to formula (3) to result in that δ(2θ) becomes about 1.0×10−5 radian, which corresponds to about two second in angle. Although the two second is a very small angle, the angular error to such an extent would have a problem in determining the thickness of the thin film with a good repeatability using the X-ray reflectance method. Especially, it is an important problem in the conventional method that there is no means for verifying how much the difference δ(2θ) is.